Paper 2026/1640 Original: eprint.iacr.org/2026/1640 ↗

Qlapoti+ and More: Optimizing Isogeny-based Signatures

Abstract

This paper presents several optimizations to Qlapoti (Asiacrypt'25), an ideal-finding procedure at the heart of modern isogeny-based signature schemes. We apply these optimizations to the Qlapoti-based NIST Round-2 SQIsign implementation from Asiacrypt'25. Together, they accelerate the Qlapoti procedure by approximately \(1.6\times\) to \(5.3\times\), depending on the parameter set and implementation. Under the Broadwell benchmark, compared with the baseline implementation in Asiacrypt'25, our optimizations achieve key-generation speedups of \(1.29\times\), \(2.23\times\), and \(1.54\times\), and signing speedups of \(1.23\times\), \(1.79\times\), and \(1.43\times\), at NIST security levels~1, 3, and~5, respectively. Our techniques also apply to the Qlapoti-optimized PRISM implementation (PKC'25, Journal of Cryptology), for which we introduce an additional tailored optimizations. Under the Broadwell benchmark, compared with the baseline implementation in JoC using Qlapoti, our improvements translate into key-generation speedups of \(1.22\times\), \(1.87\times\), and \(1.46\times\), and signing speedups of \(1.47\times\), \(1.90\times\), and \(1.60\times\), at NIST security levels~1, 3, and~5, respectively.